Alok is older than Malvika. Gyan is older than Malvika but younger than Alok.…

20172017

Alok is older than Malvika. Gyan is older than Malvika but younger than Alok. Kamal is younger than Rashmi and Malvika. Malvika is older than Rashmi. Whose age is exactly in the middle of the five?

  1. A.

    Gyan

  2. B.

    Malvika

  3. C.

    Alok

  4. D.

    Rashmi

Attempted by 14 students.

Show answer & explanation

Correct answer: B

In a linear-ordering puzzle, every comparative statement ("X is older/taller/senior than Y") is first converted into a strict inequality. Inequalities that share a common person are then chained together into one total order, and the middle element is read directly off that order.

  1. Statement 1, "Alok is older than Malvika", gives Alok > Malvika.

  2. Statement 2, "Gyan is older than Malvika but younger than Alok", extends the chain to Alok > Gyan > Malvika.

  3. Statement 3, "Kamal is younger than Rashmi and Malvika", places Kamal below both Rashmi and Malvika, though his rank relative to Rashmi alone still needs Rashmi's position fixed in the chain.

  4. Statement 4, "Malvika is older than Rashmi", extends the chain to Alok > Gyan > Malvika > Rashmi; combined with Statement 3 (Kamal below Rashmi), the complete chain is Alok > Gyan > Malvika > Rashmi > Kamal.

Cross-check by testing the final order Alok > Gyan > Malvika > Rashmi > Kamal against every original statement: Alok > Malvika holds; Alok > Gyan > Malvika holds; Kamal is younger than both Rashmi and Malvika (Kamal is last) holds; and Malvika > Rashmi holds. All four statements are satisfied, so this order is the unique solution.

With five people in the order Alok (1st) > Gyan (2nd) > Malvika (3rd) > Rashmi (4th) > Kamal (5th), the 3rd position is exactly the middle, so Malvika's age is exactly in the middle.

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